A monolithic transducer can be used to illuminate a defect with ultrasound in order to non-destructively detect it. Structural integrity (SI) analysis would then require the characterization of the defect’s physical natures (e.g., location, shape, size, and orientation angle) to predict the remaining life of a structure. If a defect cannot be accurately characterized, a worst-case scenario where the defect will most rapidly fail the structure has to be assumed. Therefore, the absence of accurate defect characterization could cause unnecessary repair or replacement of structures, putting not only money but also time, labor, and natural resources at waste.
For the past decade, the world has seen a huge rise in using ultrasound arrays as an NDT technique that enables defect detecting, sizing, and imaging. An ultrasound array, evolved from the traditional single-element ultrasonic transducer which can only perform A-scans (measuring time-domain signals of a full-waveform), has several individually connected elements. This feature enables it to perform many different types of scanning, including but not limited to A-scans, plane B-scans, focused B-scans, and sector scans and C-scans, offering great flexibility and abilities to perform rapid testing . Alternatively, post-processing algorithms such as Total Focusing Method (TFM) can be used on a full set of scan data to perform high-resolution imaging.
Due to the diffraction of waves, the imaging resolution of ultrasound array for small defects drastically decreases as the sizes of defects get closer to the wavelength of the
ultrasound in use, leaving high uncertainty to defect characterization. Fig. 1(a) compares FTM imaging results of two machined notches with dimensions 3.75×2.5 and 3.75×1.25 respectively (unit: mm). Note that the two images are seen with hardly any difference since the wavelength of the ultrasound used is 2.5mm. As shown in Fig. 1(b), the scattering matrices of the same notches are distinct, suggesting the great potentials scattering matrix possesses. In fact, defect characterization based on scattering matrix has been proved to be an effective approach for small defects (typically 1-2 wavelengths).
Fig. 1. The (a) FTM results and (b) scattering matrices of two notches dimensions 3.75×2.5 and 3.75×1.25 respectively (unit: mm). 
Seeing the potentials, many studies have been carried out to further develop this approach. Velichko et al.  sought to understand the nature of scattering matrix information and suggested Bayes’ statistical approach to retrieve defect parameters such as lengths and aspect ratios. Along with their findings, a defect manifold was also produced, onto which characterization could be performed by projecting experimental measurements. Bai et al.  trained machine learning (ML) models basing on a scattering matrix database and compared its ability to characterize defects with the Bayes’ statistical approach. It is also realized that the reduction in signal amplitude due to unfavorably orientated defects causes a huge increase in the uncertainty to the results. Bai et al.  have proposed to use locality preserving projection (LPP) to mitigate said limitation.
The objective of this project is to carry out fundamental research on two main issues.
- Discover and study defects with certain features that obscure characterization procedure
Characterisation of some types of defects or defect features come with high uncertainty. For instance, it is hard to distinguish sharp cracks from non-sharp ones. The first step into the proposed research would be to identify the scenarios where characterization uncertainty can be improved. In addition, the scattering matrix nature of such features should be thoroughly studied by collecting data from experiments as well as running virtual models. 
- Develope characterisation scheme for defects with such features
The studies given above offer great insights on retrieving defect parameters out of scattering matrices by implementing ML or LPP. These methods can potentially be the key to characterize defect features such as defect acuity. Carrying out studies around them would be the first priority of the proposed research.
- Bai, L., Velichko, A., & Drinkwater, B. W. (2018). Ultrasonic defect characterisation-Use of amplitude, phase, and frequency information. Citation: The Journal of the Acoustical Society of America, 143, 349. https://doi.org/10.1121/1.5021246
- Velichko A, Bai L,Drinkwater BW. 2017 Ultrasonic defectcharacterization using parametric-manifoldmapping.Proc.R.Soc.A473: 20170056.http://dx.doi.org/10.1098/rspa.2017.0056
- Bai, L., Le Bourdais, F., Miorelli, R., Calmon, P., Velichko, A., & Drinkwater, B. W. (2021). Ultrasonic Defect Characterization Using the Scattering Matrix: A Performance Comparison Study of Bayesian Inversion and Machine Learning Schemas. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 68(10), 3143–3155. https://doi.org/10.1109/TUFFC.2021.3084798
- Bai, L., Liu, M., Liu, N., Su, X., Lai, F., & Xu, J. (2022). Dimensionality reduction of ultrasonic array data for characterization of inclined defects based on supervised locality preserving projection. Ultrasonics, 119, 106625. https://doi.org/10.1016/j.ultras.2021.106625
- Zhang, J., Drinkwater, B.W. & Wilcox, P.D. The Use of Ultrasonic Arrays to Characterize Crack-Like Defects. J Nondestruct Eval 29, 222–232 (2010). https://doi.org/10.1007/s10921-010-0080-6